JEE Main 2016 (2)

Algebra Level 4

Given that $f(x)=x^{2}-px+q$ has has two prime numbers as roots and $p+q=11$ where $p$ is an odd positive integer.

$f(1)+f(2)+f(3)+f(4)+\cdots+f(48)$

If the value of the above expression is $A$ , then find $\dfrac{A}{16}-11$ .